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**Combustion Modeling in FLUENT**

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**Outline Applications Overview of Combustion Modeling Capabilities**

Chemical Kinetics Gas Phase Combustion Models Discrete Phase Models Pollutant Models Combustion Simulation Guidelines

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Applications Wide range of homogeneous and heterogeneous reacting flows Furnaces Boilers Process heaters Gas turbines Rocket engines Predictions of: Flow field and mixing characteristics Temperature field Species concentrations Particulates and pollutants Temperature in a gas furnace CO2 mass fraction Stream function

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**Aspects of Combustion Modeling**

Combustion Models Dispersed Phase Models Premixed Partially premixed Nonpremixed Droplet/particle dynamics Heterogeneous reaction Devolatilization Evaporation Governing Transport Equations Mass Momentum (turbulence) Energy Chemical Species Radiative Heat Transfer Models Pollutant Models

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**Combustion Models Available in FLUENT**

Gas phase combustion Generalized finite rate formulation (Magnussen model) Conserved scalar PDF model (one and two mixture fractions) Laminar flamelet model (V5) Zimont model (V5) Discrete phase model Turbulent particle dispersion Stochastic tracking Particle cloud model (V5) Pulverized coal and oil spray combustion submodels Radiation models: DTRM, P-1, Rosseland and Discrete Ordinates (V5) Turbulence models: k-, RNG k-, RSM, Realizable k- (V5) and LES (V5) Pollutant models: NOx with reburn chemistry (V5) and soot

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**Modeling Chemical Kinetics in Combustion**

Challenging Most practical combustion processes are turbulent Rate expressions are highly nonlinear; turbulence-chemistry interactions are important Realistic chemical mechanisms have tens of species, hundreds of reactions and stiff kinetics (widely disparate time scales) Practical approaches Reduced chemical mechanisms Finite rate combustion model Decouple reaction chemistry from turbulent flow and mixing Mixture fraction approaches Equilibrium chemistry PDF model Laminar flamelet Progress variable Zimont model

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**Generalized Finite Rate Model**

Chemical reaction process described using global mechanism. Transport equations for species are solved. These equations predict local time-averaged mass fraction, mj , of each species. Source term (production or consumption) for species j is net reaction rate over all k reactions in mechanism: Rjk (rate of production/consumption of species j in reaction k) is computed to be the smaller of the Arrhenius rate and the mixing or “eddy breakup” rate. Mixing rate related to eddy lifetime, k /. Physical meaning is that reaction is limited by the rate at which turbulence can mix species (nonpremixed) and heat (premixed).

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**Setup of Finite Rate Chemistry Models**

Requires: List of species and their properties List of reactions and reaction rates FLUENT V5 provides this info in a mixture material database. Chemical mechanisms and physical properties for the most common fuels are provided in database. If you have different chemistry, you can: Create new mixtures. Modify properties/reactions of existing mixtures.

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**Generalized Finite Rate Model: Summary**

Advantages: Applicable to nonpremixed, partially premixed, and premixed combustion Simple and intuitive Widely used Disadvantages: Unreliable when mixing and kinetic time scales are comparable (requires Da >>1). No rigorous accounting for turbulence-chemistry interactions Difficulty in predicting intermediate species and accounting for dissociation effects. Uncertainty in model constants, especially when applied to multiple reactions.

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**Conserved Scalar (Mixture Fraction) Approach: The PDF Model**

Applies to nonpremixed (diffusion) flames only Assumes that reaction is mixing-limited Local chemical equilibrium conditions prevail. Composition and properties in each cell defined by extent of turbulent mixing of fuel and oxidizer streams. Reaction mechanism is not explicitly defined by you. Reacting system treated using chemical equilibrium calculations (prePDF). Solves transport equations for mixture fraction and its variance, rather than species transport equations. Rigorous accounting of turbulence-chemistry interactions.

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**Mixture Fraction Definition**

The mixture fraction, f, can be written in terms of elemental mass fractions as: where Zk is the elemental mass fraction of some element, k. Subscripts F and O denote fuel and oxidizer inlet stream values, respectively. For simple fuel/oxidizer systems, the mixture fraction represents the fuel mass fraction in a computational cell. Mixture fraction is a conserved scalar: Reaction source terms are eliminated from governing transport equations.

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**Systems That Can be Modeled Using a Single Mixture Fraction**

Fuel/air diffusion flame: Diffusion flame with oxygen-enriched inlets: System using multiple fuel inlets: 60% CH4 40% CO f = 1 21% O2 79% N2 f = 0 35% O2 65% N2 f = 0 60% CH4 40% CO f = 1 35% O2 65% N2 f = 0 60% CH4 20% CO 10% C3H8 10% CO2 f = 1 21% O2 79% N2 f = 0 60% CH4 20% CO 10% C3H8 10% CO2 f = 1

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**Equilibrium Approximation of System Chemistry**

Chemistry is assumed to be fast enough to achieve equilibrium. Intermediate species are included.

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**PDF Modeling of Turbulence-Chemistry Interaction**

Fluctuating mixture fraction is completely defined by its probability density function (PDF). p(V), the PDF, represents fraction of sampling time when variable, V, takes a value between V and V + V. p(f) can be used to compute time-averaged values of variables that depend on the mixture fraction, f: Species mole fractions Temperature, density

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**PDF Model Flexibility Nonadiabatic systems: Second conserved scalar:**

In real problems, with heat loss or gain, local thermo-chemical state must be related to mixture fraction, f, and enthalpy, h. Average quantities now evaluated as a function of mixture fraction, enthalpy (normalized heat loss/gain), and the PDF, p(f). Second conserved scalar: With second scalar in FLUENT, you can model: Two fuel streams with different compositions and single oxidizer stream (visa versa) Nonreacting stream in addition to a fuel and an oxidizer Co-firing a gaseous fuel with another gaseous, liquid, or coal fuel Firing single coal with two off-gases (volatiles and char burnout products) tracked separately

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**Mixture Fraction/PDF Model: Summary**

Advantages: Predicts formation of intermediate species. Accounts for dissociation effects. Accounts for coupling between turbulence and chemistry. Does not require the solution of a large number of species transport equations Robust and economical Disadvantages: System must be near chemical equilibrium locally. Cannot be used for compressible or non-turbulent flows. Not applicable to premixed systems.

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**The Laminar Flamelet Model**

Extension of the mixture fraction PDF model to moderate chemical nonequilibrium Turbulent flame modeled as an ensemble of stretched laminar, opposed flow diffusion flames Temperature, density and species (for adiabatic) specified by two parameters, the mixture fraction and scalar dissipation rate Recall that for the mixture fraction PDF model (adiabatic), thermo-chemical state is function of f only c can be related to the local rate of strain

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**Laminar Flamelet Model (2)**

Statistical distribution of flamelet ensemble is specified by the PDF P(f,c), which is modeled as Pf (f) Pc (c), with a Beta function for Pf (f) and a Dirac-delta distribution for Pc (c) Only available for adiabatic systems in V5 Import strained flame calculations prePDF or Sandia’s OPPDIF code Single or multiple flamelets Single: user specified strain, a Multiple: strained flamelet library, 0 < a < aextinction a=0 equilibrium a= aextinction is the maximum strain rate before flame extinguishes Possible to model local extinction pockets (e.g. lifted flames)

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**The Zimont Model for Premixed Combustion**

Thermo-chemistry described by a single progress variable, Mean reaction rate, Turbulent flame speed, Ut, derived for lean premixed combustion and accounts for Equivalence ratio of the premixed fuel Flame front wrinkling and thickening by turbulence Flame front quenching by turbulent stretching Differential molecular diffusion For adiabatic combustion, The enthalpy equation must be solved for nonadiabatic combustion

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Discrete Phase Model Trajectories of particles/droplets/bubbles are computed in a Lagrangian frame. Exchange (couple) heat, mass, and momentum with Eulerian frame gas phase Discrete phase volume fraction must < 10% Although the mass loading can be large No particle-particle interaction or break up Turbulent dispersion modeled by Stochastic tracking Particle cloud (V5) Rosin-Rammler or linear size distribution Particle tracking in unsteady flows (V5) Model particle separation, spray drying, liquid fuel or coal combustion, etc. Continuous phase flow field calculation Particle trajectory calculation Update continuous phase source terms

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**Particle Dispersion: The Stochastic Tracking Model**

Turbulent dispersion is modeled by an ensemble of Monte-Carlo realizations (discrete random walks) Particles convected by the mean velocity plus a random direction turbulent velocity fluctuation Each trajectory represents a group of particles with the same properties (initial diameter, density etc.) Turbulent dispersion is important because Physically realistic (but computationally more expensive) Enhances stability by smoothing source terms and eliminating local spikes in coupling to the gas phase Coal particle tracks in an industrial boiler

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**Particle Dispersion: The Particle Cloud Model**

Track mean particle trajectory along mean velocity Assuming a 3D multi-variate Gaussian distribution about this mean track, calculate particle loading within three standard deviations Rigorously accounts for inertial and drift velocities A particle cloud is required for each particle type (e.g. initial d,r etc.) Particles can escape, reflect or trap (release volatiles) at walls Eliminates (single cloud) or reduces (few clouds) stochastic tracking Decreased computational expense Increased stability since distributed source terms in gas phase BUT decreased accuracy since Gas phase properties (e.g. temperature) are averaged within cloud Poor prediction of large recirculation zones

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**Particle Tracking in Unsteady Flows**

Each particle advanced in time along with the flow For coupled flows using implicit time stepping, sub-iterations for the particle tracking are performed within each time step For non-coupled flows or coupled flows with explicit time stepping, particles are advanced at the end of each time step

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**Coal/Oil Combustion Models**

Coal or oil combustion modeled by changing the modeled particle to Droplet - for oil combustion Combusting particle - for coal combustion Several devolatilization and char burnout models provided. Note: These models control the rate of evolution of the fuel off-gas from coal/oil particles. Reactions in the gas (continuous) phase are modeled with the PDF or finite rate combustion model.

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**NOx Models NOx consists of mostly nitric oxide (NO).**

Precursor for smog Contributes to acid rain Causes ozone depletion Three mechanisms included in FLUENT for NOx production: Thermal NOx - Zeldovich mechanism (oxidation of atmospheric N) Most significant at high temperatures Prompt NOx - empirical mechanisms by De Soete, Williams, etc. Contribution is in general small Significant at fuel rich zones Fuel NOx - Empirical mechanisms by De Soete, Williams, etc. Predominant in coal flames where fuel-bound nitrogen is high and temperature is generally low. NOx reburn chemistry (V5) NO can be reduced in fuel rich zones by reaction with hydrocarbons

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**Soot modeling in FLUENT**

Two soot formation models are available: One-step model (Khan and Greeves) Single transport equation for soot mass fraction Two-Step model (Tesner) Transport equations for radical nuclei and soot mass fraction concentrations Soot formation modeled by empirical rate constants where, C, pf, and F are a model constant, fuel partial pressure and equivalence ratio, respectively Soot combustion (destruction) modeled by Magnussen model Soot affects the radiation absorption Enable Soot-Radiation option in the Soot panel

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**Combustion Guidelines and Solution Strategies**

Start in 2D Determine applicability of model physics Mesh resolution requirements (resolve shear layers) Solution parameters and convergence settings Boundary conditions Combustion is often very sensitive to inlet boundary conditions Correct velocity and scalar profiles can be critical Wall heat transfer is challenging to predict; if known, specify wall temperature instead of external convection/radiation BC Initial conditions While steady-state solution is independent of the IC, poor IC may cause divergence due to the number and nonlinearity of the transport equations Cold flow solution, then gas combustion, then particles, then radiation For strongly swirling flows, increase the swirl gradually

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**Combustion Guidelines and Solution Strategies (2)**

Underrelaxation Factors The effect of under-relaxation is highly nonlinear Decrease the diverging residual URF in increments of 0.1 Underrelax density when using the mixture fraction PDF model (0.5) Underrelax velocity for high bouyancy flows Underrelax pressure for high speed flows Once solution is stable, attempt to increase all URFs to as close to defaults as possible (and at least 0.9 for T, P-1, swirl and species (or mixture fraction statistics)) Discretization Start with first order accuracy, then converge with second order to improve accuracy Second order discretization especially important for tri/tet meshes Discrete Phase Model - to increase stability, Increase number of stochastic tracks (or use particle cloud model) Decrease DPM URF and increase number of gas phase iterations per DPM

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**Combustion Guidelines and Solution Strategies (3)**

Magnussen model Defaults to finite rate/eddy-dissipation (Arrhenius/Magnussen) For nonpremixed (diffusion) flames turn off finite rate Premixed flames require Arrhenius term so that reactants don’t burn prematurely May require a high temperature initialization/patch Use temperature dependent Cp’s to reduce unrealistically high temperatures Mixture fraction PDF model Model of choice if underlying assumptions are valid Use adequate numbers of discrete points in look up tables to ensure accurate interpolation (no affect on run-time expense) Use beta PDF shape

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**Combustion Guidelines and Solution Strategies (4)**

Turbulence Start with standard k-e model Switch to RNG k-e , Realizable k-e or RSM to obtain better agreement with data and/or to analyze sensitivity to the turbulence model Judging Convergence Residuals should be less than 10-3 except for T, P-1 and species, which should be less than 10-6 The mass and energy flux reports must balance Monitor variables of interest (e.g. mean temperature at the outlet) Ensure contour plots of field variables are smooth, realistic and steady

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Concluding Remarks FLUENT V5 is the code of choice for combustion modeling. Outstanding set of physical models Maximum convenience and ease of use Built-in database of mechanisms and physical properties Grid flexibility and solution adaption A wide range of reacting flow applications can be addressed by the combustion models in FLUENT. Make sure the physical models you are using are appropriate for your application.

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